when use BaseHTTPMiddleware can't catch BackgroundTasks exceptions

[YuQibing]

The starting point for issues should usually be a discussion...

https://github.com/encode/starlette/discussions

when i add LoggingMiddleware, if i add_task but miss name args, can't catch exception if i comment add_middleware ,can get exception

---

from fastapi import FastAPI, Request, BackgroundTasks, HTTPException
from fastapi.responses import JSONResponse
from starlette.middleware.base import BaseHTTPMiddleware
from starlette.middleware.exceptions import ExceptionMiddleware
from starlette.middleware.cors import CORSMiddleware
from starlette.middleware.errors import ServerErrorMiddleware

async def generic_exception_handler(request: Request, exc: Exception):
    print("!!!exception")
    return JSONResponse(
        status_code=500,
        content={"message": "aaaa"},
    )

class LoggingMiddleware(BaseHTTPMiddleware):
    async def dispatch(self, request: Request, call_next):
        print(f"Request URL: {request.url}")
        response = await call_next(request)
        print(f"Response Status: {response.status_code}")
        return response

app = FastAPI()

app.add_middleware(LoggingMiddleware)

app.add_exception_handler(Exception, generic_exception_handler)

async def background_task(name: str):
    1/0

@app.get("/")
async def run_background_task(background_tasks: BackgroundTasks):
    background_tasks.add_task(background_task)
    return {"message": "Background task started"}

when i add LoggingMiddleware, if i add_task but miss name args, can't catch exception if i comment add_middleware ,can get exception can u help me..

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